An inexact stochastic optimization model for agricultural irrigation management with a case study in China

In this study, an inexact stochastic optimization model (ITSOM) is developed for agricultural irrigation management with a case study in China. Functional intervals are introduced into the modeling framework to much accurately address the spatial and temporal variation of system components. According to the results of case study, the developed model shows effectiveness in dealing with functional information of system parameters, and brings no difficulty in obtaining optimal water allocation patterns. It is indicated that the surface water resource (i.e. Heshui River) has better be used as the major source, and proper exploration of groundwater can curtail the related expense and further increase the system net benefit. Among eight farms, hybrid rice farm is going to obtain the greatest amount of water than the others, while watermelon farm has the priority to get water due to its highest benefit and penalty rate. In comparison, water allocations to rapeseed and tea farms are to be minimal within the respective fluctuation ranges. Scenario analysis is also conducted to clarify the differences between ITSOM and a conventional interval two-stage stochastic programming (ITSP) model. A total of 60 scenarios are initiated respectively linking to 60 monthly ITSP models for the entire planning horizon. The results show that the optimal objective function values of all ITSP models always fall into the range of that obtained from ITSOM. As each ITSP solution can only correspond to the system condition under a certain time point, it is highly vulnerable to system variation.     

A dual two-stage stochastic model for flood management with inexact-integer analysis under multiple uncertainties

This study introduces a hybrid optimization approach for flood management under multiple uncertainties. An inexact two-stage integer programming (ITIP) model and its dual formation are developed by integrating the concepts of mixed-integer and interval-parameter programming techniques into a general framework of two-stage stochastic programming. The proposed approach provides a linkage to pre-defined management policies, deals with capacity-expansion planning issues, and reflects various uncertainties expressed as probability distributions and discrete intervals for a flood management system. Penalties are imposed when the policies are violated. The marginal costs are determined based on dual formulation of the ITIP model, and their effects on the optimal solutions are investigated. The developed model is applied to a case study of flood management. The solutions of binary variables represent the decisions of flood-diversion–capacity expansion within a multi-region, multi-flow-level, and multi-option context. The solutions of continuous variables are related to decisions of flood diversion toward different regions. The solutions of dual variables indicate the decisions of marginal costs associated with the resources of regions’ capacity, water availability, and allowable diversions. The results show that the proposed approach could obtain reliable solutions and adequately support decision making in flood management.     

A stochastic model reduction method for nonlinear unconfined flow with multiple random input fields

In this paper we present a stochastic model reduction method for efficiently solving nonlinear unconfined flow problems in heterogeneous random porous media. The input random fields of flow model are parameterized in a stochastic space for simulation. This often results in high stochastic dimensionality due to small correlation length of the covariance functions of the input fields. To efficiently treat the high-dimensional stochastic problem, we extend a recently proposed hybrid high-dimensional model representation (HDMR) technique to high-dimensional problems with multiple random input fields and integrate it with a sparse grid stochastic collocation method (SGSCM). Hybrid HDMR can decompose the high-dimensional model into a moderate M-dimensional model and a few one-dimensional models. The moderate dimensional model only depends on the most M important random dimensions, which are identified from the full stochastic space by sensitivity analysis. To extend the hybrid HDMR, we consider two different criteria for sensitivity test. Each of the derived low-dimensional stochastic models is solved by the SGSCM. This leads to a set of uncoupled deterministic problems at the collocation points, which can be solved by a deterministic solver. To demonstrate the efficiency and accuracy of the proposed method, a few numerical experiments are carried out for the unconfined flow problems in heterogeneous porous media with different correlation lengths. The results show that a good trade-off between computational complexity and approximation accuracy can be achieved for stochastic unconfined flow problems by selecting a suitable number of the most important dimensions in the M-dimensional model of hybrid HDMR.     

A practical reliability-based method for assessing soil liquefaction potential

The current simplified methods for assessing soil liquefaction potential use a deterministic safety factor in order to judge whether liquefaction will occur or not. However, these methods are unable to determine the liquefaction probability related to a safety factor. An answer to this problem can be found by reliability analysis. This paper presents a reliability analysis method based on the popular Seed'85 liquefaction analysis method. This reliability method uses the empirical acceleration attenuation law in the Taiwan area to derive the probability density distribution function (PDF) and the statistics for the earthquake-induced cyclic shear stress ratio (CSR). The PDF and the statistics for the cyclic resistance ratio (CRR) can be deduced from some probabilistic cyclic resistance curves. These curves are produced by the regression of the liquefaction and non-liquefaction data from the Chi-Chi earthquake and others around the world, using, with minor modifications, the logistic model proposed by Liao [J. Geotech. Eng. 114 (1988) 389]. The CSR and CRR statistics are used in conjunction with the first order and second moment method, to calculate the relation between the liquefaction probability, the safety factor and the reliability index. Based on the proposed method, the liquefaction probability related to a safety factor can be easily calculated. The influence of some of the soil parameters on the liquefaction probability can be quantitatively evaluated.     

A simplified stochastic model for infiltration into a heterogeneous soil forced by random precipitation

A simplified stochastic infiltration model is presented, aimed at representing the rainfall-runoff transformation in the presence of heterogeneity in the soil and with precipitation as a random variable with complex temporal evolution. Such a model is based on a simple water mass balance of a surface soil layer, considered as a non-linear reservoir. The explicit inclusion of spatial heterogeneity allows the model to be used in sub-grid parametrizations at a variety of scales, from the distributed modelling of the hydrological response of small watersheds to the representation of surface mass fluxes in General Circulation Models. An approximate solution procedure is developed, which allows the estimation of statistical moments of the soil effective saturation and runoff inside discrete time steps where the hydraulic saturated conductivity and the rainfall intensity are taken as random variables with known probability density functions. As a first test of the proposed model, two different simulations, relative to two soils with different hydraulic conductivity distributions, are presented and discussed. A year long record of hourly averaged rainfall intensities, as measured by a tipping bucket gauge in Central Italy, is taken as the main input. The main finding is that the non-linear nature of the soil filter is such that, for random precipitation intensity, the coefficient of variation of the runoff is always higher than that of precipitation. Such a non-linear variability enhancement, due mainly to the threshold character of the soil mass balance equation, tends to be slightly dampened by the variability of the hydraulic saturated conductivity.     

安装速度相关型消能器结构直接基于位移可靠度的抗震设计方法

考察了大震作用下安装速度相关型消能器结构的薄弱层层间位移可靠度指标增大系数与原无控结构薄弱层层间位移可靠度指标、第一振型附加阻尼比和粘弹性材料损耗因子之间的定量关系,提出了该类有控结构直接基于位移可靠度的抗震设计步骤。     

Development and application of a stochastic optimization model for groundwater management: crop pattern and conjunctive use consideration

The need for irrigation water in arid and semi-arid regions is mostly supplied by groundwater. Furthermore, the agricultural development in these areas is not generally based on a comprehensive plan, which can cause aquifers depletion. On the other hand, to properly manage an aquifer and to have an optimal crop plan, the stochastic nature of the different parameters of a groundwater system such as groundwater recharge and water demands should be taken into consideration. In this paper, we develop an explicit stochastic optimization model for Firouzabad aquifer in Iran. This formulation is based on the first and second moment analysis for groundwater head which has been initially proposed for surface water resources management by Fletcher and Ponnambalam. We extend the model to create a new random withdrawal policy for conjunctive use setting in which the randomness in available precipitation is taken into account. The interesting point is that the model provides the respective probabilities of shortage and surplus without imposing the extra decision variables into the optimization model. A genetic-based algorithm is used to solve the stochastic nonlinear and non-convex formulation. The outcome results indicate that the current crop pattern should be changed, that is, the allocated areas of some crops have to be meaningfully reduced. Finally, to validate our model efficiency, we demonstrate that how much close the statistical characteristics obtained from the optimization model are to those estimated from the Monte Carlo simulation. Furthermore, the optimal benefits obtained using the proposed optimization model are as suitable as the benefits achieved using the corresponding Monte Carlo-based optimization model.     

直管损伤识别的一种简化方法

本文首先讨论了将直管中三维频散波问题简化为一维定型波问题的条件。在此条件下讨论了将管中全波场分离为单向波场的方法。由此提出了使用敲击方法检测直管损伤是否存在和判断损伤程度的两个简化模型：连续损伤模型,用于描述直管在有限长度上刚度的改变;简化裂缝模型,用于近似描述裂缝自由面效应。基于这两个模型提出了直管损伤的简化反演方法,并通过数值算例详细讨论了此法的可行性和灵敏度。在结语中简要讨论了进一步研究工作。     

带加强层高层建筑结构地震作用的简化算法

采用振型分解反应谱法计算带加强层的高层、超高层建筑的地震作用时,通常需要考虑高阶振型的影响,于此类周期比较长、高阶振型影响显著的结构,往往需要考虑较多的振型,计算过程较为复杂.通过对带加强层高层建筑结构在侧向荷载作用下的受力和变形特点进行分析发现带加强层高层建筑结构在侧向荷载作用下内筒及外柱等构件的变形及内力在加强层处...     

A Monte Carlo study of rainfall forecasting with a stochastic model

A procedure for short-term rainfall forecasting in real-time is developed and a study of the role of sampling on forecast ability is conducted. Ground level rainfall fields are forecasted using a stochastic space-time rainfall model in state-space form. Updating of the rainfall field in real-time is accomplished using a distributed parameter Kalman filter to optimally combine measurement information and forecast model estimates. The influence of sampling density on forecast accuracy is evaluated using a series of a simulated rainfall events generated with the same stochastic rainfall model. Sampling was conducted at five different network spatial densities. The results quantify the influence of sampling network density on real-time rainfall field forecasting. Statistical analyses of the rainfall field residuals illustrate improvement in one hour lead time forecasts at higher measurement densities.     

A simplified method of constructing fragility curves for highway bridges

Fragility curves are found to be useful tools for predicting the extent of probable damage. They show the probability of highway structure damage as a function of strong motion parameters, and they allow the estimation of a level of damage probability for a known ground motion index. In this study, an analytical approach was adopted to develop the fragility curves for highway bridges based on numerical simulation. Four typical RC bridge piers and two RC bridge structures were considered, of which one was a non‐isolated system and the other was an isolated system, and they were designed according to the seismic design code in Japan. From a total of 250 strong motion records, selected from Japan, the United States, and Taiwan, non‐linear time history analyses were performed, and the damage indices for the bridge structures were obtained. Using the damage indices and ground motion parameters, fragility curves for the four bridge piers and the two bridge structures were constructed assuming a lognormal distribution. It was found that there was a significant effect on the fragility curves due to the variation of structural parameters. The relationship between the fragility curve parameters and the over‐strength ratio of the structures was also obtained by performing a linear regression analysis. It was observed that the fragility curve parameters showed a strong correlation with the over‐strength ratio of the structures. Based on the observed correlation between the fragility curve parameters and the over‐strength ratio of the structures, a simplified method was developed to construct the fragility curves for highway bridges using 30 non‐isolated bridge models. The simplified method may be a very useful tool to construct the fragility curves for non‐isolated highway bridges in Japan, which fall within the same group and have similar characteristics. Copyright © 2003 John Wiley & Sons, Ltd.     

A stochastic optimization framework for the restoration of an over-exploited aquifer

ABSTRACT

This study investigates the impact of hydraulic conductivity uncertainty on the sustainable management of the aquifer of Lake Karla, Greece, using the stochastic optimization approach. The lack of surface water resources in combination with the sharp increase in irrigation needs in the basin over the last 30 years have led to an unprecedented degradation of the aquifer. In addition, the lack of data regarding hydraulic conductivity in a heterogeneous aquifer leads to hydrogeologic uncertainty. This uncertainty has to be taken into consideration when developing the optimization procedure in order to achieve the aquifer’s sustainable management. Multiple Monte Carlo realizations of this spatially-distributed parameter are generated and groundwater flow is simulated for each one of them. The main goal of the sustainable management of the ‘depleted’ aquifer of Lake Karla is two-fold: to determine the optimum volume of renewable groundwater that can be extracted, while, at the same time, restoring its water table to a historic high level. A stochastic optimization problem is therefore formulated, based on the application of the optimization method for each of the aquifer’s multiple stochastic realizations in a future period. In order to carry out this stochastic optimization procedure, a modelling system consisting of a series of interlinked models was developed. The results show that the proposed stochastic optimization framework can be a very useful tool for estimating the impact of hydraulic conductivity uncertainty on the management strategies of a depleted aquifer restoration. They also prove that the optimization process is affected more by hydraulic conductivity uncertainty than the simulation process.

Editor Z.W. Kundzewicz; Guest editor S. Weijs     

随机有限断层法模拟中强地震近场强震动的参数影响研究

介绍了模拟地震动时程的随机有限断层法及近年来对该方法的改进,改进后的随机有限断层法适合模拟中强地震;比较了不同场地方位角的中强地震近场地震动时程与平均伪加速度反应谱(PSA);定量分析了中强地震近场地震动模拟结果的参数敏感性. 结果表明：不同场地方位角的中强地震近场PSA在短周期部分差别较大;应力降是模型中最重要的参数,其对反应谱短周期部分影响最大;几何扩散系数对PSA的整体影响也较为明显. 将随机有限断层法应用到工程安全性评价工作中时,应当重点关注对反应谱短周期部分影响较大的应力降和该区域的几何扩散系数,同时要调查该区域优势场地方位角的分布,更加合理地控制中强地震近场强震动的模拟.     

基于修正岩土体强度参数的简化纽马克位移法地震滑坡危险性快速评估技术

地震滑坡危险性评估可为震后应急响应等提供科学的决策依据。纽马克位移法可不依赖同震滑坡编目快速评估同震滑坡危险性。工程岩体物理力学参数是该方法的核心参数之一,但其赋值过于单一,难以反映复杂地质背景下岩体强度的空间差异性。针对上述问题,本文在分析地震滑坡影响因子的基础上,选择距断层距离、高程和距水系距离作为影响岩体强度的评价指标并建立岩体强度评价模型,获得区域岩体强度修正系数,进而修正传统方法的临界加速度。结合震后的即时地震动峰值加速度,采用简化纽马克位移法计算边坡累积位移,开展地震滑坡危险性快速评估,并以汶川M_W7.9地震的地震滑坡危险性评估为例验证本文方法。结果表明,相对于传统方法,本文方法划分的地震滑坡危险区与同震滑坡分布更加一致。     

A stochastic model for optimal operation of inter-basin water allocation systems: a case study

This paper presents a new methodology for optimal operation of inter-basin water transfer systems by conjunctive use of surface water resources in water donor basin and groundwater resources in water receiving basin. To incorporate the streamflow uncertainty, an integrated stochastic dynamic programming (ISDP) model is developed. In the ISDP, the monthly inflow to the reservoir in the water donor basin, the water storage of the reservoir, and the water storage of the aquifer in the water receiving basin are considered as state variables. A water allocation optimization model is embedded in the main structure of ISDP and a new ensemble streamflow prediction model based on K-nearest-neighbourhood algorithm is also developed and linked to the ISDP. By using a new reoptimization process, the ISDP model provides monthly policies for water allocation to users in water donor and receiving basins. As water users can form a coalition to increase their benefits, several solution concepts in cooperative game theory, namely Nash–Harsanyi, Shapley, Nucleolus, Weak Nucleolus, Proportional Nucleolus, Separable Costs Remaining Benefits (SCRBs) and Minimum Costs Remaining Savings are utilized to determine the profit of each water user. In the last step, stakeholders make negotiation over these solution concepts using the Fallback bargaining theory to reach a unanimous agreement on the final distribution of the total benefit. The methodology is applied to an inter-basin water transfer project and the results show that the Shapley and SCRB solutions concepts can provide better distributions for the total benefit and the total benefit of water users is increased by a factor of 1.6 when they participate in a grand coalition.     

Multiobjective fuzzy optimization for sustainable groundwater management using particle swarm optimization and analytic element method

Groundwater management involves conflicting objectives as maximization of discharge contradicts the criteria of minimum pumping cost and minimum piping cost. In addition, available data contains uncertainties such as market fluctuations, variations in water levels of wells and variations of ground water policies. A fuzzy model is to be evolved to tackle the uncertainties, and a multiobjective optimization is to be conducted to simultaneously satisfy the contradicting objectives. Towards this end, a multiobjective fuzzy optimization model is evolved. To get at the upper and lower bounds of the individual objectives, particle Swarm optimization (PSO) is adopted. The analytic element method (AEM) is employed to obtain the operating potentio metric head. In this study, a multiobjective fuzzy optimization model considering three conflicting objectives is developed using PSO and AEM methods for obtaining a sustainable groundwater management policy. The developed model is applied to a case study, and it is demonstrated that the compromise solution satisfies all the objectives with adequate levels of satisfaction. Sensitivity analysis is carried out by varying the parameters, and it is shown that the effect of any such variation is quite significant. Copyright © 2015 John Wiley & Sons, Ltd.     

偏心结构非线性地震反应分析的一种简化方法

本文建立了基于结构状态方程和偏心结构体系的层剪力-扭矩等效屈服EYST面概念的求解平扭耦联非线性地震反应的分离-予估-修正递推算法，编制了相应的计算程序。通过与三个单层偏心结构模型的破坏性地震模拟试验结果的对比，验证了小变形阶段平-扭耦联地震反应算法的实用性和可靠性。算例表明，该程序数据处理量小，运算快捷，便于应用。     

Propagation of uncertainty from rainfall to runoff: A case study with a stochastic rainfall generator

We explore the impact of uncertainties in the spatial–temporal distribution of rainfall on the prediction of peak discharge in a typical mountain basin. To this end, we use a stochastic generator previously developed for rainfall downscaling, and we estimate the basin response by adopting a semi-distributed hydrological model. The results of the analysis provide information on the minimum rainfall resolution needed for operational flood forecasting, and confirm the sensitivity of peak discharge estimates to errors in the determination of the power spectrum of the precipitation field.     

钢筋混凝土耗能减振结构的地震损伤简化分析方法

本文提出了钢筋混凝土耗能减振结构地震反应和损伤分析的简化方法.首先给出了考虑轴力变化效应的耗能减振结构Pushoverr分析方法,以及结构等价阻尼比ζ的计算公式;其次,结合文献[12]中提出的"三水准"地震损伤性能目标,提出了耗能减振结构基于能力谱法的地震反应、损伤分析与性能设计方法;最后,对一座设置金属屈服型耗能器的四层钢筋混凝土框架结构进行了地震反应和损伤分析.